{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "%matplotlib inline\n",
    "seaborn.set_style(\"whitegrid\")\n",
    "\n",
    "from procedures import FindEffort, dh\n",
    "update_figs = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def FindTopTerms(ε, h̄, ρ):\n",
    "    \"\"\"Find terms in the optimal top tax rate formula \n",
    "            (in the limit as z* -> infty)\"\"\"\n",
    "    \n",
    "    l = FindEffort(ε, h̄, 0, \"pp\")\n",
    "    dh_val = dh(l, ε, h̄)\n",
    "    e_dh = np.exp(dh_val)\n",
    "        \n",
    "    # Pareto coefficient adjustment factor\n",
    "    δ_ρ_term = (1 - l)/(1 + l*(e_dh - 1))*(1 - e_dh**(1 - ρ))\n",
    "    δ_ρ = (1 - δ_ρ_term)**(-1)\n",
    "    \n",
    "    # MSWW adjustment factor\n",
    "    A = (1 + e_dh**(- ρ) * (1 - l)/l)**(-1)\n",
    "    μL = 1/(1 + l*(e_dh - 1))\n",
    "    μH = e_dh*μL\n",
    "    δ_g = 1 + (μH-1)*A + (μL-1)*(1-A)\n",
    "    \n",
    "    # Elasticity\n",
    "    X_term = l*(1 - l)*e_dh + l**2 + ((1 - l)*e_dh + l)/(e_dh - 1)\n",
    "    X = ((1 - 2*l)/(1 - l) + 1/ε - 1 + 1/ε*dh_val*X_term)**(-1)\n",
    "\n",
    "    e = X/(1 -  1/e_dh) * (1 - e_dh**(1 - ρ)) + X*(ρ-1)/ρ * e_dh**(1 - ρ)        \n",
    "\n",
    "    return e, δ_ρ, δ_g\n",
    "\n",
    "def FindTopRates(ε, h̄, ρ, g):\n",
    "    e, δ_ρ, δ_g = FindTopTerms(ε_pp, h̄_pp, ρ)\n",
    "    Rearrange = lambda x: x/(1 + x)\n",
    "    \n",
    "    τ_pp = Rearrange((1 - δ_g * g)/(δ_ρ * ρ * e))\n",
    "    τ_er = Rearrange((1 - g)/(δ_ρ * ρ * e))\n",
    "    τ_m = Rearrange((1 - g)/(ρ * e))\n",
    "    \n",
    "    return τ_pp, τ_er, τ_m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Baseline calibration values\n",
    "ε_pp = 0.3740369510517757\n",
    "h̄_pp = 45.08880335177867\n",
    "ρ    = 2.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gV = np.linspace(0, 0.6, 100)\n",
    "τV = np.zeros((3, len(gV)))\n",
    "for i in range(len(gV)):\n",
    "    τV[:, i] = FindTopRates(ε_pp, h̄_pp, ρ, gV[i])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "fs = 20\n",
    "ax.plot(gV, τV[0, :],\"k-\", lw=3, label=\"optimal\")\n",
    "ax.plot(gV, τV[1, :],\"k--\",lw=3, label=\"exogenous risk (SCPE)\")\n",
    "ax.plot(gV, τV[2, :],\"k:\", lw=3, label=\"full insurance, Mirrlees (SCPE)\")\n",
    "\n",
    "ax.set_xlabel(\"marginal social welfare weight of top earners\", fontsize=20)\n",
    "xticks = np.linspace(0.7, 0, 8).round(decimals=1)\n",
    "ax.set_xticks(xticks)\n",
    "ax.set_xticklabels([str(x) for x in xticks], fontsize=fs-4)\n",
    "ax.set_xlim([0, gV[-1]])\n",
    "\n",
    "ax.set_ylabel(\"top tax rate\", fontsize=20)\n",
    "yticks = np.linspace(0, 0.9, 10).round(decimals=1)\n",
    "ax.set_yticks(yticks)\n",
    "ax.set_yticklabels([str(y) for y in yticks], fontsize=fs-4)\n",
    "ax.set_ylim([0, 0.8])\n",
    "\n",
    "plt.legend(fontsize=fs-2)\n",
    "\n",
    "if update_figs:\n",
    "    plt.savefig('fig4.eps', bbox_inches='tight', format = 'eps', dpi = 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
